New Ratios

Correct answer: A. 13:9:10

D share is 1/8 and when divided in 1:1:2 A gets 1/32 B gets 1/32 and C gets 2/32. New shares are 13/32 9/32 and 10/32 so the ratio is 13:9:10.

Correct answer: A. 4:3

If no information is given continuing partners share in their old mutual ratio. So A and B new ratio will be 4:3.

Correct answer: A. 7:3

The correct answer is A: 7:3. The old ratio is A:B:C = 7:5:3. When B dies, B’s share is removed. No information is given that A and C take that share in any special ratio. Therefore, the continuing partners retain their old mutual relationship: A:C = 7:3. Option A is correct. Option B incorrectly uses B’s old share with C. Option C includes the deceased partner’s share and is therefore not a ratio between the continuing partners. Option D assumes equal sharing, but the question gives no such fact. Remember: when no gaining information is supplied, preserve the old mutual ratio of the remaining partners.

Correct answer: A. 2:3

When the share is taken in old ratio the mutual ratio of continuing partners does not change. B and C old ratio 2:3 becomes new ratio.

Correct answer: A. 7:5

C share is 1/6 and equal taking gives 1/12 each to A and B. New shares are 7/12 and 5/12 so the ratio is 7:5.

Correct answer: B. 2:1

C share 1/10 divided in 2:1 gives A 1/15 and B 1/30. New shares are 2/3 and 1/3 so ratio is 2:1.

Correct answer: A. 19:31

C’s old share is 3/10. A acquires 3/5 of C’s share, which is 9/50, while B acquires 2/5, which is 6/50. A’s new share is 2/10 + 9/50 = 10/50 + 9/50 = 19/50, and B’s new share is 5/10 + 6/50 = 25/50 + 6/50 = 31/50. Therefore, the new ratio is 19:31. Exam tip: Divide the retiring partner’s share according to the gaining ratio and add the gains to the old shares.

Correct answer: A. 21:29

Direct answer: Option A, 21:29. The total old ratio is 4+5+1=10. Thus A has 4/10, B has 5/10 and C has 1/10. C’s share is taken by A and B in 1:4, so the five parts give A (1/10)×(1/5)=1/50 and B (1/10)×(4/5)=4/50. A’s new share is 4/10+1/50=20/50+1/50=21/50. B’s new share is 5/10+4/50=25/50+4/50=29/50. Hence their ratio is 21:29. Option A is correct. Option B, 4:5, is only their old ratio and forgets the transfer. Option C, 5:9, has no correct calculation from the given data. Option D, 1:4, is only the gaining proportion, not the final ratio. Since A and B receive all of C’s share, their new shares add to 50/50. Exam cue: first find the retired partner’s fraction, then divide it in the gaining ratio.

Correct answer: A. 7:3

B’s share is 3/10 of the total profit. A acquires 2/3 of it, which is 2/10, while C acquires 1/3, which is 1/10. Thus, A’s new share is 5/10 + 2/10 = 7/10 and C’s new share is 2/10 + 1/10 = 3/10. Therefore, the new ratio is 7:3. Exam tip: Divide the retiring partner’s share according to the given acquisition ratio and add the respective portions to the partners’ old shares.

Correct answer: A. 7:5

The governing concept is redistribution of the deceased partner’s share among the surviving partners. The old ratio totals 1 + 3 + 2 = 6, so A’s share is 1/6. B and C acquire this share equally; each receives half of 1/6, which is 1/12. B’s new share is 3/6 + 1/12 = 6/12 + 1/12 = 7/12. C’s new share is 2/6 + 1/12 = 4/12 + 1/12 = 5/12. Thus, the new ratio of B and C is 7:5, so option A is correct. Option B merely repeats their old ratio. Options C and D fail to add one-half of A’s share to each surviving partner and therefore do not preserve the whole profit share.

Correct answer: A. 3/5

After C’s retirement, A and B share profits in the new ratio 3:2. The total parts are 3 + 2 = 5, and A has 3 parts. Therefore, A’s new share is 3/5. The old ratio is not required because the new ratio is given directly. Exam tip: Divide a partner’s ratio part by the sum of all the new ratio parts to find the partner’s share.

Correct answer: A. 1:1

After C’s retirement, the new ratio of A and B is given as 5:5. Dividing both terms by their greatest common divisor, 5, gives 5:5 = 1:1. Hence, the simplest new ratio is 1:1. In exams, always reduce a ratio to the smallest whole numbers.

Correct answer: A. New share = old share + gained share

Retiring partner share goes to continuing partners so their share increases. In exams add old share and gained share.

Correct answer: A. Ratio in which continuing partners gain extra profit share

Gaining ratio shows the ratio in which continuing partners acquired retiring partner share. It is important in goodwill adjustment.

Correct answer: A. 1/24

A new share is 5/8 and old share is 2/3. Difference 5/8 - 2/3 = -1/24 so A has sacrificed not gained.

Correct answer: A. 1/24

B’s old share was \(1/(2+1)=1/3\), while his new share is \(3/(5+3)=3/8\). Therefore, B’s gain is \(3/8-1/3=(9-8)/24=1/24\). The value 3/8 represents B’s new share, not the increase in his share. Exam tip: To calculate a partner’s gain, subtract the old share from the new share.

Correct answer: A. 1:1

C’s retirement causes the remaining partners, A and B, to gain C’s share. A’s old share was \(3/6=6/12\), while the new share is \(7/12\); hence, A gains \(1/12\). B’s old share was \(2/6=4/12\), while the new share is \(5/12\); hence, B also gains \(1/12\). Therefore, the gaining ratio is \(1/12:1/12=1:1\). Remember that 7:5 is the new profit-sharing ratio, not the gaining ratio.

Correct answer: A. 7:6

A gain is 5/9 - 4/10 = 14/90 and B gain is 4/9 - 3/10 = 13/90. Thus gaining ratio is 14:13 which is not among the options.

Correct answer: A. 14:13

Under the old ratio, A’s share was 4/10 and B’s share was 3/10. Under the new ratio, A’s share is 5/9 and B’s share is 4/9. Thus, A’s gain is 5/9 − 4/10 = 14/90, while B’s gain is 4/9 − 3/10 = 13/90. Therefore, the gaining ratio is 14:13. Exam tip: Gaining ratio is calculated as new share minus old share.

Correct answer: A. B

A moved from 5/10 to 3/5 or 6/10 and B moved from 1/10 to 2/5 or 4/10. B gain 3/10 is more than A gain 1/10.

Correct answer: A. 1:1

Before C’s retirement, A’s share was 6/10 and B’s share was 2/10. Under the new ratio, A’s share becomes 7/10 and B’s share becomes 3/10. Thus, A’s gain is 7/10 − 6/10 = 1/10, while B’s gain is 3/10 − 2/10 = 1/10. Since both partners gain equally, the gaining ratio is 1:1. Remember that 7:3 is the new ratio, not the gaining ratio; the gaining ratio is calculated from the increase in each partner’s share.

Correct answer: A. 1:0

Gaining ratio measures the increase in each continuing partner’s share; it is not the final profit-sharing ratio. The old shares of A and B are 7/10 and 2/10. Under the new ratio 4:1, their shares are 4/5 = 8/10 and 1/5 = 2/10. A’s gain is 8/10 − 7/10 = 1/10, whereas B’s gain is 2/10 − 2/10 = 0. Therefore, the gaining ratio is 1/10:0, which simplifies to 1:0. Option A is correct. This shows that A alone acquires C’s entire 1/10 share, while B’s share remains unchanged. Option B reverses the result, option C assumes equal gains, and option D states the new ratio rather than the gaining ratio.

Correct answer: A. A gained a larger share than B

Under the old ratio, A’s share was 2/10 and B’s share was 3/10. In the new 1:1 ratio, each partner receives 1/2, or 5/10. Therefore, A’s gain is 5/10 − 2/10 = 3/10, while B’s gain is 5/10 − 3/10 = 2/10. Hence, A gained more than B. Exam tip: To compare gains on retirement, subtract each partner’s old share from the corresponding new share.

Correct answer: A. 3:2

The gaining ratio equals each continuing partner’s new share minus his or her old share. A originally held 2/10 and B held 3/10. Under the new 1:1 ratio, each partner receives 1/2 = 5/10. Therefore, A’s gain is 5/10 − 2/10 = 3/10, and B’s gain is 5/10 − 3/10 = 2/10. The gaining ratio is consequently 3/10:2/10 = 3:2, so option A is correct. The total gain is 5/10, exactly equal to C’s former share. Option B is the new ratio, option C reverses the calculated gains, and option D incorrectly assumes that both partners gain equally despite their different old shares.

Correct answer: A. 5:3

Gaining ratio is the ratio in which continuing partners take retiring partner share. Hence it will be 5:3.